Discount means that the transaction price is lower than the face value; Premium means that the transaction price is higher than the face value. In fact, literally speaking, if it is lower than the original and initial, it is called discount, on the contrary, if it is higher than the original and initial, it is called premium. Discount and premium are compared with face value (individual financial products are fair market prices in a specific context).
The appearance of discount and premium mainly comes from the fluctuation of market price. For example, if we go to a store to buy water, we can find that the price of bottled water is the same, but when we go to some special supermarkets or snack supermarkets, we can obviously find that the prices in these places are much cheaper, because they are sold at a discount when ordering from manufacturers. If something is in short supply in the market, we often have to pay a higher price to buy it.